Sequences
Posted by Reversearp
Given that a sequence is an ordered list of values, our job is to find a way to generalize the patterns we find. We can either do that recursively where we define the next term in “terms” of the previous ones, or we can do it expicitly where any term is determined simply by its place in the sequence. There are advantages and disadvantages to both – what are they?
We will be concerned with two special sequences – arithmetic and geometric. You should be able to write both recursive and explicit formulas for both. You should also be aware of the general numerical patterns that hold for both. We also talked today about how to use sequence mode on your calculator to plot discrete graphs of sequences.
Lastly then be warned that sequences other than arithmetic and geometric will not be as easy to find generalizations for – especially explicit formulas. For example, you should have no trouble writing a recursive formula for the Fibonacci sequence, but spend a little while trying to write an explicit formula – then give up and look it up.
